Conclusion - 3D Computer Vision: Efficient Methods and Applications - page 353

approaches that aim for a reconstruction of cross-sectional surface profiles, which
were originally developed in the domain of planetary remote sensing in the mid-
dle of the twentieth century, are closely related to the shape from shading methods
developed about three decades ago in the domain of computer vision. If informa-
tion about the reflectance properties of the surface is available, intensity-based ap-
proaches may provide fairly accurate information about the surface gradients, which
in turn yield the three-dimensional surface shape. However, a drawback of most
shape from shading methods is that they only converge towards a solution if ad-
ditional constraints such as smoothness or integrability of the surface are applied.
Furthermore, the determined solution is generally not unique. Shape from shading
methods which yield a unique solution based on a partial differential equation ap-
proach are restricted to Lambertian surfaces and require a priori knowledge about
the position of local minima of the surface, which is not necessarily straightforward
to obtain.
Some of these drawbacks are alleviated when several pixel-synchronous im-
ages acquired under different illumination conditions are available for an evalua-
tion in terms of photometric stereo. The classical approach relies on three pixel-
synchronous images of the scene acquired under different illumination conditions
and yields a unique configuration of albedo and surface gradients for each pixel,
which can be computed by a pixel-wise matrix inversion procedure as long as the
surface is Lambertian. The described ratio-based photoclinometric and photometric
stereo methods relying on two pixel-synchronous images are suitable for a more
general class of reflectance functions. In contrast to the classical photometric stereo
approach, they can be used in the presence of the coplanar illumination vectors often
encountered in remote sensing scenarios.
Furthermore, an extension of the shape from shading framework to the deter-
mination of surface orientation from polarisation information has been described.
Accurate and physically well-defined polarisation models based on the Fresnel the-
ory are available for smooth dielectric surfaces. An approximate description can still
be obtained according to the refraction law for smooth, specularly reflecting metal-
lic surfaces. Rough metallic surfaces, however, have a more complex polarisation
behaviour for which no accurate physical models are available so far. Hence, we
have proposed an empirical framework to determine the dependence between the
polarisation properties of rough metallic surfaces and the observing and illumina-
tion geometry.
The third examined class of three-dimensional reconstruction methods is that of
the point spread function (PSF)-based approaches. They exploit the dependence of
the PSF on the distance between the camera and the object. Depth from defocus
approaches measure the width of the PSF and infer the object depth based on a pre-
viously determined relation between these two values. While classical PSF-based
methods assume that this dependence can be well described in terms of geometric
optics, this work has shown that an empirical approach based on a suitable calibra-
tion of the lens (which may be performed simultaneously with geometric camera
calibration) is preferable. The depth-defocus function introduced in this context has
been shown to represent the observed relation between object depth and width of